An improved direct inverse problem solver for fractal interpolation functions with applications to signal compression

A novel direct algorithm used to estimate parameters of fractal interpolation functions is proposed, and test results of its robustness and its signal compression performance are reported. The IFS fractal interpolation function (FIF) is becoming an increasingly appealing class of models of such signals as the height distribution of sea floors, seismograph, and electrocardiograph signals, due to its inherent advantages. Existing FlF-based signal compression algorithms usually use the FIF parameter estimation formula proposed by Uazel and Hayes (see IEEE Trans. Signal Processing, vo1.40, no.7, p.1724, 1992), which is based on least square-error fitting techniques and needs to calculate the derivatives of such a error measure with respect to FIF parameters. It is very inconvenient to introduce many other useful error measures in real signal processing applications, such as the Kullback entropy or the Hausdorff distance, for they may endanger the computability of the derivatives. A computationally efficient, direct algorithm for solving the inverse problem of the IFS interpolation signals is proposed. It can solve the FIF parameters from its samples without calculating the error function's derivatives. The algorithm's robustness in parameter estimation and usefulness in signal compression are shown with experimental results.